As you read this, chances are a worker-bee at the Republican National Committee is updating the "book" on Hillary Rodham Clinton. After two decades of fixating on the former first lady, senator and secretary of state, the GOP by now may already have a data trove that would make the NSA blush.

Here's a suggestion for Republicans, should Mrs. Clinton do the expected and seek the presidency: Cool it with the opposition research. It isn't what Hillary has done that should worry you. Rather, it's how she'll go about capturing the prize that eluded her in 2008.

What will be her campaign's most likely avenue of attack? The Republican "war on women." Why? Because, as the election results from Tuesday's governor's race in Virginia indicate, the Democratic attack line that President Obama used so effectively in gaining re-election is still working just fine.

President Obama used the theme to perfection last year, tarring the opposition party as insensitive and intolerant with regard to women's health, reproductive rights and civil liberties. Consider the makeup of the winning Democratic coalition in 2012. Mr. Obama lost the men's vote by 7% to Mitt Romney, the worst-ever showing for a presidential winner. (In 2008, Mr. Obama won the men's vote by 1%.) However, Mr. Obama carried the women's vote by 11%—only the second time that a net-female/minus-male formula proved successful. Bill Clinton pulled off the feat in 1996.

Without the "war on women" and its effect on turnout in the presidential election, Mr. Obama's re-election might not have occurred. Women accounted for 54% of 2012's turnout, swinging such pivotal states as Ohio (where Mr. Obama lost independents by 10% and won women by 12%) and New Hampshire (where Mr. Obama lost the men's vote by 4% and won the women's vote by 16%).

What should concern Republicans at this hour: The same scorched-earth tactic proved effective for a much more flawed candidate than Mr. Obama, Virginia Gov.-elect Terry McAuliffe. Running a relentless ad campaign savaging Republican Ken Cuccinelli as intransigent on abortion, no-fault divorce and other women's-rights issues, Mr. McAuliffe carried the unmarried women's vote by 42%, a 6% improvement on Mr. Obama's performance in 2012 and far greater than Mr. McAuliffe's 25% advantage among unmarried male voters.

How does this affect Mrs. Clinton, should she seek the presidency? She won't have much of a margin for error.

Flip three states that Mr. Obama carried by 3% or less in 2012—Florida, Ohio and Virginia—and he still wins, but with only 272 electoral votes, one more than George W. Bush in 2000. And, like Mr. Obama, Mrs. Clinton may have trouble with male voters. In the 2008 primaries, she lost the men's vote by 13% to the party's eventual nominee. Thus the Clinton campaign may feel added pressure to make sure women are in her camp.

Even if Mrs. Clinton ultimately decides not to run, any Democratic presidential nominee would be almost obliged to campaign against a GOP "war on women." The potential reward, and the proven effectiveness of the tactic, would be too hard to resist.

So how should the GOP prepare for the "war on women" allegations to come? Here are three suggestions.

First, Republicans would do well to de-emphasize social issues. They didn't do so in the 2012 campaign, when conservatives promoted concepts and crusades—including defunding Planned Parenthood and promoting the No Taxpayer Funding for Abortion Act—that were grist for the Democratic attack mill.

Should Republicans somehow gain control of Congress in 2015, they must avoid a repeat of the political lunacy of supplying ammunition for their harshest critics. On a similar note, the clueless utterances of candidates Todd Akin and Richard Mourdock on matters such as rape and abortion were gifts to the entire Democratic Party in helping confirm the "war on women" theme.

The model for success in 2012 could be found in Republican Bob McDonnell's victory in the Virginia governor's race four years ago. Mr. McDonnell is pro-life, but he campaigned as "the jobs governor." He carried the women's vote by 8%.

Second, if Mrs. Clinton runs, Republicans of all stripes should inoculate against Clinton Derangement Syndrome—the snark and vitriol that the famous couple stirs. (Democrats have a similar challenge if Jeb Bush is the Republican nominee.) That means no reliving Whitewater, Monica Lewinsky, cattle-futures trading—no cheap shots regarding ancient transgressions that didn't seem to bother a majority of the American electorate.

Mrs. Clinton stands to benefit from two tailwinds if she becomes the Democratic nominee. One would be the historic nature of her candidacy. The other would be a media free ride: Guilt-ridden reporters want to even the score after ditching her for Barack Obama in 2008. Personal insults from the GOP will prompt the media to add victimhood to her saintly profile.

The third recommendation: If Mrs. Clinton is the nominee, the GOP would be almost compelled to engage in identity politics and put a woman on the ticket. The Republican field of president hopefuls lacks a nominee-in-waiting. It also has no woman who is seen as a serious contender. Assuming that a man lands the nomination, he'll be hard-pressed to lambaste Mrs. Clinton. If you doubt that, do a Google search for "Republican," "Obama" and "racist," and see how legitimate criticism of the current presidency is met by counterclaims of bigotry and racial animus.

In 2016, the challenge for Republicans will be learning to fight back when "misogynist" replaces "racist" as the Democrats' pejorative du jour. Adding a woman to the Republican ticket would allow the presidential candidate to stay upbeat and visionary, rather than wrestle in the muck over more contentious matters like Mrs. Clinton's Benghazi testimony. Leave that to the running mate.

Some Republicans will blanch at this notion. But just as the 2016 election will be a referendum on the nation's progress during the Obama years, so too will it test the GOP's ability to learn from past Democratic successes and past Republican mistakes—one of those errors being unable to rebut the "war on women" attacks in 2012 and then watching as they worked again in Virginia a year later.

Some storms take a political party by surprise; others are easy to predict. It shouldn't take a village for the Republicans to get their act together.

Mr. Whalen is a research fellow at Stanford University's Hoover Institution.

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